Finite and Quaternary shortening calculation Finite shortening Models commonly used to constrain the structural evolution, shortening, and surface uplift of fault-related folds rely primarily on their limbs and associated planar fault geometry (Avouac et al., 1993; Suppe, 1983; Suppe and Medwedeff, 1990). For instance, line-length shortening (e.g. Dahlstrom, 1969, Supplementary Figure 1) is widely used to estimate the shortening of any particular stratigraphic horizon in a faulted section, and its relation to fold and fault geometry is, in general, well understood. However, detachment folds commonly do not bear simple structural relationships between the parameters controlling fold evolution, and depend largely on their mechanical stratigraphy (Mitra, 2002). In an attempt to resolve the complexities between different structural parameters, diverse methodologies for describing fold evolution, including growth strata and surface uplift have been developed (Bernard et al., 2007; Daëron et al., 2007; Gonzalez-Mieres and Suppe, 2012; Hardy and Poblet, 2005; Simoes et al., 2007; Storti and Poblet, 1997). These diverse approaches take advantage of the geometrical relationships between pregrowth or growth strata either from outcrops or from seismic information. In the case of the Tame Anticline however, the shallower portion of the available seismic volume do not have enough resolution to resolve the geometry of growth strata (Figure 7). Therefore, we used a simple approach similar to the excess area method (Epard and Groshong, 1993; Gonzalez- Mieres and Suppe, 2006, 2012; Wiltschko and Groshong, 2012) to calculate finite
shortening of the pre-growth and growth sequences, and also a simple formulation from the relief relationship between the deformed terraces and pregrowth strata, to discern among mechanisms for fold growth and to quantify Quaternary shortening. Assuming that during initial stages of deformation, structures are characterized by shortening accumulated by folding and internal strain (Epard and Groshong, 1993; Gonzalez-Mieres and Suppe, 2006; Wiltschko and Groshong, 2012), we calculated shortening using the excess area and the line-length methods (Supplementary Figure 1), to be able to derive the contribution of internal strain to the total shortening budget. The excess area of any particular stratigraphic horizon above its undeformed level divided by the line-length shortening of the same was first used by Chamberlin (1910) to estimate the depth to the detachment horizon (Figure 6a), using the following relationship: and, where Hd is the depth to the detachment, Asr is the excess area of each horizon above its regional or undeformed level, and is the line-length shortening, which is the difference between the length of the deformed bed ( ) and the length of the cross sectional area ( ) (Supplementary Figure 1). This formulation has been revised to consider the uncertainties associated with overestimating the depth to detachment (Grando and McClay, 2004; Mitra, 2002; Wiltschko and Groshong,
2012). For instance, Mitra (2002) suggested that overestimating the depth to detachment from Chamberlin s (1910) equation arises from not incorporating areas below the regional level or the particular undeformed level of each interpreted horizon. However, these areas commonly represent only a small fraction of the excess area and therefore cannot account for the cross sectional shortening. On the other hand, Epard and Groshong (1993) suggested that the disparity in Chamberlin s formulation arises from not considering internal strain (i.e., homogeneous strain). Epard and Groshong (1993) thus proposed that finite shortening (St) of a cross sectional area is the derivative of the excess area ( ) over the derivative of the height of the interpreted horizons ( ) from an arbitrary reference level. The fixed reference level can be used to estimate the depth to the detachment ( ), and to determine if mass has flowed into the core of the anticline (Figure 6a), where: Using the same formulation, can also be expressed in terms of the thickness of the sedimentary sequence (Hubert-Ferrari et al., 2005) or in reference to a predefined reference level (e.g., surface) (Scharer et al., 2004). We note that internal strain ( ) is below the resolution of the seismic data, but field observations of structures such as cleavage development, parasitic folding and strain hardening suggests this approach is valid (Wiltschko and Groshong, 2012). Then, line-length shortening ( ) used in (1) represents only a portion of the finite
shortening (St), and the ratio between these two is the internal strain ( ) for the cross sectional area, that can be expressed as: where the ratio of line-length and finite shortening describes the portion of finite deformation related to internal strain. Large values of internal strain are expected when the difference between Sl and St is large, and therefore a small fraction of the total strain is consumed by folding. During later stages of folding, internal strain decreases to zero. At this stage, Sl and St are expected to be of the same magnitude. Quaternary shortening Kink band migration and limb rotation are the two widely used models to describe the development of growth strata in contractional orogens (Poblet and McClay, 1996; Poblet et al., 1997; Suppe and Medwedeff, 1990). These two models make different predictions about the geometry of deformed terraces at the surface, depending upon the interplay between sedimentation and uplift rates (Scharer et al., 2006). However, cumulative deformation witnessed by recent strain markers is often difficult to document, primarily due to poor preservation of these features across the fold via erosion and surface processes. Therefore, to determine the Quaternary contribution of shortening recorded by the deformed terraces, we use two different novel approaches that might cover a wide spectrum of geological settings and can be applied to a variety of situations.
Topographic cross sectional area The topographic cross sectional method follows the simple assumption that under the cases where the original geometry of the deformed terraces is relatively well preserved across the structure (e.g. Qt2 and Qt3), topographic profiles of the terrace can be used to determine the Quaternary contribution to shortening. In our specific case, the topographic profiles were extracted from the DEM (Figure 5). The excess area of the topographic profiles is then used in equation 3, whereas the depth to detachment is the average of all the Hd values calculated on equation 1 for the pregrowth strata. Also, we considered the base of the topographic profiles not to be the aggradational surface of the basin floor, but the depth at which the mapped terraces should lie on the subsurface, according to an average deposition rate for the basin (Figure 6c). Crestal relief to finite shortening ratio In the second approach, we follow the basic premise that the spatial variation along strike in fold geometry and kinematics (i.e. shortening and crestal relief) reflects the temporal evolution of the anticline since the inception of folding (Higgins et al., 2009; Wilkerson et al., 2002). We plot the relationship between the crestal relief (CR) of each unfaulted interpreted horizon (C5, C3, C2, C1, and Intra- Guayabo) versus the calculated finite shortening (St) of the same horizon (Figure 6d) and use this relationship to estimate the cumulative shortening recorded by the deformed terraces. The shortening near the lateral terminations of the fold reflect
the recent history of deformation, and its magnitude can be equated to the millennial scale shortening, recorded by the uplifted terraces. Likewise in the first approach, involving the cross sectional area of the topography, we considered the base of the topographic profiles not to be the aggradational surface of the basin floor, but the depth at which the mapped terraces should lie on the subsurface, therefore the maximum relief of the strain markers is located at the maximum topographic relief plus the predicted depth of the horizon in the subsurface using an average deposition rate for the basin. The crestal relief to finite shortening ratio is particularly useful in situations where the terrace are poorly preserved across the fold (e.g. Qt1), or when only terrace flights are preserved. The major limitation of this method is that it will always represent the minimum finite Quaternary shortening. Supplementary Figure 1. (a) Depth interpretation of seismic section C-C (location on Figure 2). Same conventions for color coding as in Figure 7. (b) Detailed diagram showing the measurements for the finite shortening calculation on the pregrowth strata (C1 and Une formations shown as example). Line length shortening is equated as the difference between the deformed line length of the interpreted horizon (Ld), or the addition of the deformed line length of the hangingwall (hw) and footwall (fw) of the deformed horizon, and the cross section length (L). For the excess area method, the sum of all the excess areas of the interpreted horizon and a fixed reference level (see Supplementary Table 1) are used to derive the cross sectional
finite shortening. Crestal relief (Cr) for each individual unfaulted horizon was plotted against the mean shortening, solving for shortening on equation 1, to derive the relationship between crestal relief and horizontal shortening, used to determine the Quaternary shortening recorded by the deformed terraces. Supplementary Figure 2. Summary images of age modeling parameters and results for bulk densities and erosion rates for the sampled terraces. Supplementary Table 1. Values of line-length shortening (Sl), excess area (Asr) and Crestal Relief (CR) measurements for each interpreted horizon (Intra-Guayabo, C1, C2, C3, C5, Chipaque, Une, and Sub-Une) in each cross-sectional area along-strike from the southern end of the 3D seismic volume of the Tame Anticline. The reference level used in the calculations for each particular horizon is also included (from well on the study area). References Avouac, J. P., Tapponnier, P., Bai, M., You, H., and Wang, G., 1993, Active thrusting and folding along the northern Tien Shan and late Cenozoic rotation of the Tarim relative to Dzungaria and Kazakhstan: Journal of Geophysical Research, v. 98, no. B4, p. 6755-6804. Bernard, S., Avouac, J. P., Dominguez, S., and Simoes, M., 2007, Kinematics of fault-related folding derived from a sandbox experiment: J. geophys. Res, v. 112, p. B03S12. Chamberlin, R. T., 1910, The Appalachian folds of central Pennsylvania: The Journal of Geology, v. 18, no. 3, p. 228-251.
Daëron, M., Avouac, J. P., Charreau, J., and Dominguez, S., 2007, Modeling the shortening history of a fault tip fold using structural and geomorphic records of deformation: J. geophys. Res, v. 112, p. B03S13. Epard, J. L., and Groshong, R. H., 1993, Excess area and depth to detachment: AAPG BULLETIN, v. 77, p. 1291-1291. Gonzalez-Mieres, R., and Suppe, J., 2006, Relief and shortening in detachment folds: Journal of Structural Geology, v. 28, no. 10, p. 1785-1807. -, 2012, Shortening histories in active detachment fold based on area-of-relief methods, in McClay, K., Shaw, J., and Suppe, J., eds., Thrust Fault-Related Folding, Volume 94: AAPG Memoir. Grando, G., and McClay, K., 2004, Structural evolution of the Frampton growth fold system, Atwater Valley-Southern Green Canyon area, deep water Gulf of Mexico: Marine and Petroleum Geology, v. 21, no. 7, p. 889-910. Hardy, S., and Poblet, J., 2005, A method for relating fault geometry, slip rate and uplift data above fault propagation folds: Basin Research, v. 17, no. 3, p. 417-424. Higgins, S., Clarke, B., Davies, R. J., and Cartwright, J., 2009, Internal geometry and growth history of a thrust-related anticline in a deep water fold belt: Journal of Structural Geology, v. 31, no. 12, p. 1597-1611. Hubert-Ferrari, A., Suppe, J., Wang, X., and Jia, C., 2005, The Yakeng detachment fold, South Tianshan, China., in Shaw, J., Connors, C., and Suppe, J., eds., Seismic Interpretation of Contractional Fault-Related Folds, Volume 94: AAPG Memoirs, p. 110-113. Mitra, S., 2002, Structural models of faulted detachment folds: AAPG BULLETIN, v. 86, no. 9, p. 1673-1694. Poblet, J., and McClay, K., 1996, Geometry and kinematics of single-layer detachment folds: AAPG BULLETIN, v. 80, no. 7, p. 1085-1109. Poblet, J., McClay, K., Storti, F., and Muñoz, J. A., 1997, Geometries of syntectonic sediments associated with single-layer detachment folds: Journal of Structural Geology, v. 19, no. 3, p. 369-381. Scharer, K., Burbank, D., Chen, J., and Weldon II, R., 2006, Kinematic models of fluvial terraces over active detachment folds: Constraints on the growth mechanism of the Kashi-Atushi fold system, Chinese Tian Shan: Geological Society of America Bulletin, v. 118, no. 7-8, p. 1006-1021. Scharer, K., Burbank, D., Chen, J., Weldon, R., Rubin, C., Zhao, R., and Shen, J., 2004, Detachment folding in the Southwestern Tian Shan-Tarim foreland, China: shortening estimates and rates: Journal of Structural Geology, v. 26, no. 11, p. 2119-2137. Simoes, M., Avouac, J. P., Chen, Y. G., Singhvi, A. K., Wang, C. Y., Jaiswal, M., Chan, Y. C., and Bernard, S., 2007, Kinematic analysis of the Pakuashan fault tip fold, west central Taiwan: Shortening rate and age of folding inception: Journal of Geophysical Research, v. 112, no. B3, p. B03S14. Storti, F., and Poblet, J., 1997, Growth stratal architectures associated to decollement folds and fault-propagation folds. Inferences on fold kinematics: Tectonophysics, v. 282, no. 1, p. 353-373. Suppe, J., 1983, Geometry and kinematics of fault-bend folding: American Journal of science, v. 283, no. 7, p. 684-721. Suppe, J., and Medwedeff, D. A., 1990, Geometry and kinematics of fault-propagation folding: Eclogae geologicae Helvetiae, v. 83, no. 3, p. 409-453. Wilkerson, S. M., Apotria, T., and Farid, T., 2002, Interpreting the geologic map expression of contractional fault-related fold terminations: lateral/oblique ramps versus displacement gradients: Journal of Structural Geology, v. 24, no. 4, p. 593-607.
Wiltschko, D. V., and Groshong, R. H., 2012, The Chamberlin 1910 balanced section: context, contribution, and critical reassessment: Journal of Structural Geology, v. 41, p. 7-23. (Chamberlin, 1910)
0 W X Y Surface E Ld C1 Cr C1-2 Intra Guayabo C1 base level Asr C1a Asr C1b Depth (km) -4-6 -8 C1 C2 C5 Chipaque Une Sub-Une Basement a b -10 C3 Ld Une-hw Une base level Line Length Sl = Ld - L Sl = (Ld hw + Ld fw ) - L Cr Une Asr Une a Asr Une b Asr Une c L Ld Une-fw Excess Area Hd = Asr / Sl Hd = Asr i + Asr n / Sl St = Asr / Hd Supplementary Figure 1
DR2015090 Terrace Qt1 Supplementary Figure 2
DR2015090 Terrace Qt2 Supplementary Figure 2 (Cont.)
DR2015090 Terrace Qt3 Supplementary Figure 2 (Cont.)
Supplementary Table 1 Distance from southern end of 3D volume (m) Sl - Intra Guayabo (m) Sl - C1 (m) Sl - C2 (m) Sl - C3 (m) Sl - C5 (m) Sl - Chipaque (m) Sl - Une (m) Sl - Sub-Une (m) Asr - Intra Guayabo Asr -C1 (m 2 ) Asr - C2 (m 2 ) Asr -C3 (m 2 ) Asr - C5 (m 2 ) Asr - Chipaque Asr - Une (m 2 ) Asr - Sub- Une (m 2 ) CR - Intra Guayabo (m) CR - C1 (m) CR - C2 (m) CR - C3 (m) CR - C5 (m) (m 2 ) (m 2 ) 21600 0 0 0 0 0 0 0 0 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0 0 0 0 0 0 0 0 21000 0 0 0 0 0 0 0 0 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0 0 0 0 0 0 0 0 20400 0 0 0 0 0 0 0 0 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0 0 0 0 0 0 0 0 19800 0 0 0 0 0 0 0 0 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0 0 0 0 0 0 0 0 19200 1 0 0 1 1 0 0 0 6.27E+04 0.00E+00 0.00E+00 2.76E+04 2.31E+04 0.00E+00 0.00E+00 0.00E+00 36 0 0 27 21 0 0 0 18600 9 2 2 18 17 0 0 0 3.79E+05 7.96E+04 6.18E+04 2.76E+05 2.54E+05 0.00E+00 0.00E+00 0.00E+00 136 48 48 160 155 0 0 0 18000 17 10 11 27 26 0 0 0 6.66E+05 4.25E+05 3.83E+05 4.39E+05 3.91E+05 0.00E+00 0.00E+00 0.00E+00 195 125 115 205 200 0 0 0 17400 31 16 20 35 33 0 0 0 9.73E+05 4.41E+05 4.68E+05 6.06E+05 5.69E+05 0.00E+00 0.00E+00 0.00E+00 275 180 195 244 240 0 0 0 16800 39 32 41 69 63 420 131 0 1.25E+06 7.57E+05 7.52E+05 6.81E+05 7.01E+05 5.05E+05 4.96E+05 0.00E+00 335 275 295 355 340 347 347 0 16200 60 45 61 104 114 377 292 213 1.77E+06 1.34E+06 1.27E+06 1.20E+06 1.11E+06 9.07E+05 8.84E+05 5.86E+05 390 345 350 450 428 585 420 310 15600 68 41 45 65 67 421 161 185 1.64E+06 1.06E+06 1.06E+06 9.88E+05 8.57E+05 6.11E+05 7.37E+05 4.98E+05 397 325 340 425 425 590 345 290 15000 55 49 59 67 71 351 390 236 1.74E+06 1.30E+06 1.14E+06 1.11E+06 1.07E+06 8.37E+05 8.02E+05 5.17E+05 395 345 385 445 455 490 325 375 14400 62 64 69 100 102 374 370 290 1.88E+06 1.27E+06 1.43E+06 1.21E+06 1.12E+06 8.48E+05 8.81E+05 5.21E+05 415 395 425 535 530 415 330 355 13800 65 73 75 101 103 278 398 233 2.22E+06 1.53E+06 1.56E+06 1.14E+06 1.27E+06 9.48E+05 9.91E+05 6.20E+05 420 425 460 535 530 455 415 415 13200 69 66 72 96 79 342 381 337 2.25E+06 1.56E+06 1.70E+06 1.65E+06 1.37E+06 1.14E+06 1.10E+06 7.88E+05 440 440 465 540 490 510 490 325 12600 75 65 72 73 79 352 436 357 2.00E+06 1.39E+06 1.30E+06 1.30E+06 1.23E+06 9.30E+05 9.23E+05 6.26E+05 460 435 470 470 485 465 435 380 12000 84 83 91 87 104 423 437 396 1.80E+06 1.26E+06 1.25E+06 1.12E+06 1.05E+06 8.21E+05 8.54E+05 5.90E+05 485 450 480 487 510 380 400 180 11400 93 151 184 176 176 440 487 445 1.98E+06 1.46E+06 1.28E+06 1.27E+06 1.12E+06 9.23E+05 9.50E+05 6.03E+05 505 580 610 570 565 400 275 310 10800 109 183 182 186 192 523 537 415 2.29E+06 1.57E+06 1.53E+06 1.45E+06 1.36E+06 1.04E+06 1.04E+06 6.67E+05 540 540 595 575 582 490 400 390 10200 169 239 253 252 232 498 508 443 2.49E+06 1.78E+06 1.79E+06 1.71E+06 1.56E+06 1.06E+06 1.02E+06 7.85E+05 565 590 620 610 607 525 455 370 9600 165 283 286 379 358 579 505 515 2.45E+06 1.81E+06 1.63E+06 1.64E+06 1.48E+06 1.08E+06 1.01E+06 6.88E+05 590 595 605 635 615 495 385 240 9000 242 318 343 318 318 483 536 549 2.57E+06 1.77E+06 1.66E+06 1.46E+06 1.36E+06 1.04E+06 1.00E+06 7.03E+05 690 595 575 530 535 440 420 410 8400 185 267 285 306 325 397 462 521 2.61E+06 1.78E+06 1.69E+06 1.50E+06 1.38E+06 1.05E+06 1.01E+06 6.63E+05 690 595 580 580 590 460 415 375 7800 211 249 282 264 257 383 421 480 2.59E+06 1.74E+06 1.68E+06 1.57E+06 1.39E+06 1.07E+06 1.09E+06 6.70E+05 710 625 630 615 555 460 360 250 7200 166 245 283 266 252 112 366 584 2.76E+06 1.93E+06 1.85E+06 1.70E+06 1.49E+06 1.16E+06 1.12E+06 7.22E+05 662 625 615 645 587 425 380 230 6600 166 180 199 198 150 110 370 515 2.32E+06 2.09E+06 1.83E+06 1.68E+06 1.37E+06 1.12E+06 9.55E+05 7.01E+05 675 620 605 595 515 415 375 390 6000 128 136 132 142 160 85 458 560 2.27E+06 1.62E+06 1.56E+06 1.53E+06 1.40E+06 1.02E+06 1.02E+06 7.21E+05 610 575 590 570 565 380 370 330 5400 112 168 170 129 121 141 392 468 2.07E+06 1.76E+06 1.74E+06 1.44E+06 1.28E+06 9.98E+05 1.02E+06 6.95E+05 570 630 605 505 470 435 445 340 4800 89 89 103 108 119 73 273 379 1.68E+06 1.39E+06 1.42E+06 1.19E+06 1.05E+06 8.45E+05 9.39E+05 6.36E+05 490 470 485 435 417 345 420 350 4200 35 30 36 24 27 16 40 43 9.20E+05 6.98E+05 6.93E+05 5.66E+05 5.02E+05 4.62E+05 4.65E+05 3.74E+05 280 265 250 205 205 170 200 200 3600 8 20 5 16 2 25 21 26 2.89E+05 2.07E+05 2.10E+05 1.10E+05 1.30E+05 1.47E+05 1.09E+05 1.08E+05 117 155 70 70 30 180 185 185 3000 0 2 1 0 0 0 0 0 1.59E+04 4.45E+04 2.70E+04 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 12 35 20 0 0 0 0 0 2400 0 0 0 0 0 0 0 0 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0 0 0 0 0 0 0 0 1800 0 0 0 0 0 0 0 0 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0 0 0 0 0 0 0 0 1200 0 0 0 0 0 0 0 0 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0 0 0 0 0 0 0 0 600 0 0 0 0 0 0 0 0 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0.00E+00 0 0 0 0 0 0 0 0 CR - Chipaque (m) CR - Une (m) CR - Sub-Une (m)